| Topic: |
Science > Physics |
| User: |
"Timtro" |
| Date: |
25 Oct 2003 06:51:34 PM |
| Object: |
Angular momentum |
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man sits
on a stoll free to ratate without friction and is spun around while he holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of rotation.
Obviously the man will go faster because of this, but when I calculated the
initial and final kinetic energies, they were VERY differant. Where did all
that extra energy come from? Or did I calculate the energy wrong?
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| User: "Gregory L. Hansen" |
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| Title: Re: Angular momentum |
26 Oct 2003 06:02:55 AM |
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In article <a0Emb.2757$7B1.1868@news04.bloor.is.net.cable.rogers.com>,
Timtro <timtro@rogers.com> wrote:
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man sits
on a stoll free to ratate without friction and is spun around while he holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of rotation.
Obviously the man will go faster because of this, but when I calculated the
initial and final kinetic energies, they were VERY differant. Where did all
that extra energy come from? Or did I calculate the energy wrong?
Did you recalculate the moment of inertia when the man changed the
distribution of his masses?
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé
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| User: "Timtro" |
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| Title: Re: Angular momentum |
26 Oct 2003 02:22:20 PM |
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Didn't have to. The moment given was for the man and the chair only, and an
initial angular speed. From that, combined with the radi, I was able to
calculate the tangencial velocity in both states, which in turn, I converted
back to angular velocity for part A of the question. For part B where it
asked to give the Ke of both states (weights at 1m and then at 0.3m) I
simply did this:
Ke=Sum(fi)=1/2(I Va^2)+m Vt^2 -> where Va is angular velocity and Vt is
tangencial.
Note the 1/2 is not included in the second term because there were two
weights. Was this wrong?
Thanks
"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:bngd5f$r5g$1@hood.uits.indiana.edu...
In article <a0Emb.2757$7B1.1868@news04.bloor.is.net.cable.rogers.com>,
Timtro <timtro@rogers.com> wrote:
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man
sits
on a stoll free to ratate without friction and is spun around while he
holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of
rotation.
Obviously the man will go faster because of this, but when I calculated
the
initial and final kinetic energies, they were VERY differant. Where did
all
that extra energy come from? Or did I calculate the energy wrong?
Did you recalculate the moment of inertia when the man changed the
distribution of his masses?
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé
.
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| User: "" |
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| Title: Re: Angular momentum |
27 Oct 2003 10:09:40 AM |
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In article <02Wmb.16704$7B1.1716@news04.bloor.is.net.cable.rogers.com>, "Timtro" <timtro@rogers.com> writes:
Didn't have to. The moment given was for the man and the chair only, and an
initial angular speed. From that, combined with the radi, I was able to
calculate the tangencial velocity in both states, which in turn, I converted
back to angular velocity for part A of the question. For part B where it
asked to give the Ke of both states (weights at 1m and then at 0.3m) I
simply did this:
Ke=Sum(fi)=1/2(I Va^2)+m Vt^2 -> where Va is angular velocity and Vt is
tangencial.
That formulation sounds good.
You did remember to recompute Vt as Va * r when you reduced radius
from 1m to .3m, right?
You did use I as the moment of inertia of the man+stool alone and
did not include the weights, right?
Just how big is Vt? If he's spinning fast, it is not implausible
that he will have to exert 100N ~= 20 pounds-force to reel those
weights in against a ~1.5g centrifugal force. And one revolution
every second or two should give you centrifugal forces in that
ballpark.
Presumably we are making the simplifying assumption that the
man's moment of inertia is in his body and we can ignore any
repositioning of his arms. (Even though that simplifying assumption
is almost certainly wildly counter-factual).
Standard operating procedure in homework is to simplify away any
imponderables for which measurements were not provided. It is
good form to explicitly note this on your answer. But use restraint.
The teacher may resent being presented with a laundry list of
nit-picking assumptions that should have been obvious.
[bottom posting snipped]
John Briggs
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| User: "Sam Wormley" |
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| Title: Re: Angular momentum |
25 Oct 2003 07:59:53 PM |
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Timtro wrote:
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man sits
on a stoll free to ratate without friction and is spun around while he holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of rotation.
Obviously the man will go faster because of this, but when I calculated the
initial and final kinetic energies, they were VERY differant. Where did all
that extra energy come from? Or did I calculate the energy wrong?
Angular Momentum
http://scienceworld.wolfram.com/physics/AngularMomentum.html
Look at equation (2)
L is constant
Kinetic Energy
http://scienceworld.wolfram.com/physics/KineticEnergy.html
Look at equation (11)
Total Energy is conserved, but Kinetic Energy is not
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| User: "Richard" |
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| Title: Re: Angular momentum |
25 Oct 2003 07:05:46 PM |
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Timtro wrote:
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man sits
on a stoll free to ratate without friction and is spun around while he holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of rotation.
Obviously the man will go faster because of this, but when I calculated the
initial and final kinetic energies, they were VERY differant. Where did all
that extra energy come from? Or did I calculate the energy wrong?
The man had to do work to reel in the weights.
.
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| User: "Timtro" |
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| Title: Re: Angular momentum |
26 Oct 2003 04:21:40 AM |
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That much energy comes just from putting his arms in? It couldent possibly
take in the order of 100N to pull a couple of lousy 3kg weights into your
sides could it? It seems to be the only explaination, certinly the first
that I thought of, but I dismised it because it seemed so unreal. This is
almost enough to get me into a bar, just to try it ;) Wouldent I be the life
of the party! hehe!
"Richard" <no_mail_no_spam@yahoo.com> wrote in message
news:3F9B0FDA.9EAB1F05@yahoo.com...
Timtro wrote:
I'm sorry to bother you all with this question. I was just playing
around
with a problem I found in a book. It is a simple problem where in a man
sits
on a stoll free to ratate without friction and is spun around while he
holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of
rotation.
Obviously the man will go faster because of this, but when I calculated
the
initial and final kinetic energies, they were VERY differant. Where did
all
that extra energy come from? Or did I calculate the energy wrong?
The man had to do work to reel in the weights.
.
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| User: "tadchem" |
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| Title: Re: Angular momentum |
26 Oct 2003 11:35:50 AM |
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"Timtro" <timtro@rogers.com> wrote in message
news:UeNmb.55103$3f.18874@twister01.bloor.is.net.cable.rogers.com...
That much energy comes just from putting his arms in? It couldent
possibly
take in the order of 100N to pull a couple of lousy 3kg weights into your
sides could it?
There is something seriously wrong with your math. Energy is measured in
Joules, not Newtons.
Tom Davidson
Richmond, VA
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| User: "Timtro" |
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| Title: Re: Angular momentum |
27 Oct 2003 06:01:47 PM |
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My math is fine, my expression is not. I meant Jules.
"tadchem" <tadchemNOSPAM@comcast.net> wrote in message
news:jo-dndlT5PQgdAaiRVn-gA@comcast.com...
"Timtro" <timtro@rogers.com> wrote in message
news:UeNmb.55103$3f.18874@twister01.bloor.is.net.cable.rogers.com...
That much energy comes just from putting his arms in? It couldent
possibly
take in the order of 100N to pull a couple of lousy 3kg weights into
your
sides could it?
There is something seriously wrong with your math. Energy is measured in
Joules, not Newtons.
Tom Davidson
Richmond, VA
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| User: "G=EMC^2 Glazier" |
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| Title: Re: Angular momentum |
28 Oct 2003 03:34:15 PM |
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Angular momentum is used by nature so that objects don't just fall into
each other because of their mutual attraction.(Earth sun etc) We call
this outward energy "centrifugal force" However I go with Mach,and he
told me centrifugal force is naive thinking. Bert PS Mach is one of
my "ideals"
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| User: "Repeating Decimal" |
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| Title: Re: Angular momentum |
25 Oct 2003 08:14:59 PM |
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in article 3F9B0FDA.9EAB1F05@yahoo.com, Richard at
wrote on 10/25/03 5:05 PM:
Timtro wrote:
I'm sorry to bother you all with this question. I was just playing around
with a problem I found in a book. It is a simple problem where in a man sits
on a stoll free to ratate without friction and is spun around while he holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of rotation.
Obviously the man will go faster because of this, but when I calculated the
initial and final kinetic energies, they were VERY differant. Where did all
that extra energy come from? Or did I calculate the energy wrong?
The man had to do work to reel in the weights.
One of my pet interests is fly fishing and the cazsting required to put a
fly out where you want it to go. The process is similar to that used in a
whip.
A heavy line, ususally tapered in thickness, is flicked out using arm
motion. After the flick (cast) is completed, arm motion ceases. The line
continues to travel. The speed of the tip can increast (in the case of a
whip) close to the speed of sound. Often, the whip cracks or a fly gets
flicked of the leader.
How does the tip get speeded up? Aside from incidental losses to sound and
the like, is mechanical energy conserved? Is momentum conserved? If not,
where does extra momentum com from?
If there is a discussion on the subject here, and if no one figures it out
(an unlikely situation) I will reveal the mechanisms in a week or two.
Bill
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| User: "tj Frazir" |
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| Title: Re: Angular momentum |
25 Oct 2003 08:33:37 PM |
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Centrifical force is converted to speed.
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| User: "MorituriMax" |
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| Title: Re: Angular momentum |
25 Oct 2003 09:46:30 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:17398-3F9B2471-326@storefull-2158.public.lawson.webtv.net...
Centrifical.. .. ..
no he wants an answer from someone with an education.
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| User: "Timtro" |
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| Title: Re: Angular momentum |
26 Oct 2003 04:37:02 AM |
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If i had to guess, i would say that the tip accelarates as a consequance of:
A: force provided by the jerk backwords to "snap" the whip/fly.
B: I can picture it as being simolar to an angular rotation problem with th
body rotating at one end. For example, placing a uniform rod with a pivot at
one end, hanging from a ceeling. As a result of the angular motion when the
system is released, the tip of the rod will accelerate faster than gravity.
But the whip is not ridgid like a rod, and it is not simply under the
influance of gravity. Also, the segments of the whip do not accelerate
uniformly, this causes the whip to retard in such a way the the tip falls
behind the midpoint in the whips trajectory (this is when tall towers begind
to fall, they break apart). As the segments of the whip begin to reach full
extension (starting near the hilt of the whip), the whips radius of rotation
becomes smaller and smaller, and finally at the tip, when the radius is at
its smallest, the energy reaches a maximum, and then the signature "snap"
when the tip inverts and collides with itself.
"Repeating Decimal" <salmonfry@sbcglobal.net> wrote in message
news:BBC06E41.28F9%salmonfry@sbcglobal.net...
in article 3F9B0FDA.9EAB1F05@yahoo.com, Richard at
no_mail_no_spam@yahoo.com
wrote on 10/25/03 5:05 PM:
Timtro wrote:
I'm sorry to bother you all with this question. I was just playing
around
with a problem I found in a book. It is a simple problem where in a man
sits
on a stoll free to ratate without friction and is spun around while he
holds
two 3kg weights. we are given the moment of inertia of the man+stool,
initial speed and the fact that the weights are 1m from the axis of
rotation. The man then contracts his arms to 0.3m from the axis of
rotation.
Obviously the man will go faster because of this, but when I calculated
the
initial and final kinetic energies, they were VERY differant. Where did
all
that extra energy come from? Or did I calculate the energy wrong?
The man had to do work to reel in the weights.
One of my pet interests is fly fishing and the cazsting required to put
a
fly out where you want it to go. The process is similar to that used in a
whip.
A heavy line, ususally tapered in thickness, is flicked out using arm
motion. After the flick (cast) is completed, arm motion ceases. The line
continues to travel. The speed of the tip can increast (in the case of a
whip) close to the speed of sound. Often, the whip cracks or a fly gets
flicked of the leader.
How does the tip get speeded up? Aside from incidental losses to sound and
the like, is mechanical energy conserved? Is momentum conserved? If not,
where does extra momentum com from?
If there is a discussion on the subject here, and if no one figures it out
(an unlikely situation) I will reveal the mechanisms in a week or two.
Bill
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